Hi folks. (Hi)

Got a Set question here:

"Use Cantor's diagonalization method to show that the set of all infinite strings of the letters {a,b} is not countable."

So here's what I have already tried:

I assumed it was denumerable to begin with and I want to produce a number that's not on the list in order to prove it's actually not countable.

First I figure I'll depict the string in a list... and I want to have 3 elements to do a proper diagonalization, but I couldn't get it to work well since I only have a and b...

S1 = L11 L12 L13

S2 = L21 L22 L23

S3 = L31 L32 L33

So, X = X1 X2 ...

if L11 = a, X1 = a, otherwise X1 = b

if L22 = a, X2 = a, otherwise X2 = b

Honestly I'm not really sure what to do at this point. (Worried)